Finite Group Databasebeta

← C2×#22620297 #33955233

Subgroups — C2×#22620297 #33955233

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989217C211yesmaximal, characteristic, complemented
2C2×#17989162C211yesmaximal, characteristic
3#22620297C2116yesmaximal, direct product factor
4C2×#17988954C211yesmaximal, characteristic, complemented
5C2×#17988948C211yesmaximal, characteristic, complemented
6C2×#17988947C211yesmaximal, characteristic, complemented
7C2×#17988944C211yesmaximal, characteristic, complemented
8C2×#17988943C211yesmaximal, characteristic, complemented
9C2×#17988937C211yesmaximal, characteristic, complemented
10C2×#17988936C211yesmaximal, characteristic, complemented
11C2×#17988587C211yesmaximal, characteristic
12C2×#17988594C211yesmaximal, characteristic, complemented
13C2×#17988582C211yesmaximal, characteristic
14C2×#103×D73C211yesmaximal, characteristic, complemented
15C2×#17988544C211yesmaximal, characteristic, complemented
16C2×#491×C73C211yesmaximal, characteristic, complemented
17C22×#11924029C2211yescharacteristic
18C22×Q8×D73C2211yescharacteristic
19C22×#11924011C2211yescharacteristic
20C22×C8×D73C2211yescharacteristic
21#17989217—24no—
22#17989217C2218yescomplemented
23#17989162—24no—
24#17989162C2218yes—
25C2×#14556591C2211yescharacteristic
26C2×#14556590—21no—
27C2×#14556590C2211yescharacteristic
28C2×#14556589C2211yescharacteristic
29C2×#14556582C2211yescharacteristic
30C2×#14556581—21no—
31C2×#14556580C2211yescharacteristic
32C2×#14556579C2211yescharacteristic
33C2×#14556576—21no—
34C2×#14556576—21no—
35C2×#14556571—21no—
36C2×#14556569—21no—
37C2×#14556569—21no—
38C2×#14556569—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548C2211yescharacteristic
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988954C2218yescomplemented
43#17988948C2218yescomplemented
44#17988947C2218yescomplemented
45#17988944C2218yescomplemented
46#17988943C2218yescomplemented
47#17988937C2218yescomplemented
48#17988936C2218yescomplemented
49#17988594C2218yescomplemented
50#17988587C2218yes—
51#17988582C2218yes—
52C2×#14556516C2211yescharacteristic
53C2×#14556516C2211yescharacteristic
54C2×#14556515C2211yescharacteristic
55C2×#14556515C2211yescharacteristic
56C2×#14556515C2211yescharacteristic
57C2×#14556515C2211yescharacteristic
58C2×#14556514C2211yescharacteristic
59C2×#14556514C2211yescharacteristic
60#103×D73C2218yescomplemented
61C2×#14556513C2211yescharacteristic
62C2×#14556513C2211yescharacteristic
63C2×#14556511C2211yescharacteristic
64C2×#14556511C2211yescharacteristic
65#17988544C2218yescomplemented
66C2×#14556501C2211yescharacteristic
67C2×C4×#10596831C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C2×C4⋊Q8×C73C2211yescharacteristic
70C2×#125×C73C2211yescharacteristic
71#491×C73C2218yescomplemented
72C2×#103×C73C2211yescharacteristic
73C2×#103×C73C2211yescharacteristic
74C2×#103×C73C2211yescharacteristic
75C2×#103×C73C2211yescharacteristic
76C2×#97×C73C2211yescharacteristic
77C2×#11924029—22no—
78C2×#11924029—24no—
79C2×#11924029—24no—
80C2×#11924029C2314yes—
81C22×Dic146—21no—
82C22×Dic146—21no—
83C22×Dic146—21no—
84C22×Dic146C2311yescharacteristic
85C2×Q8×D73—22no—
86C2×Q8×D73—24no—
87C2×Q8×D73—24no—
88C2×Q8×D73C2314yes—
89C22×D292—21no—
90C22×D292C2311yescharacteristic
91C22×C4×D73—21no—
92C22×C4×D73—21no—
93C22×C4×D73—21no—
94C22×C4×D73C2311yescharacteristic
95C2×#11924011—24no—
96C2×#11924011C2314yes—
97C22×#10596831C2311yescharacteristic
98C22×#10596831C2311yescharacteristic
99C2×C8×D73—24no—
100C2×C8×D73C2314yes—
101#14556591—22no—
102#14556591C2314yes—
103#14556590—28no—
104#14556590—22no—
105#14556590C2314yes—
106#14556589—22no—
107#14556589C2314yes—
108#14556582—22no—
109#14556582C2314yes—
110#14556581—28no—
111#14556580—22no—
112#14556580C2314yes—
113#14556579—22no—
114#14556579C2314yes—
115#14556576—28no—
116#14556576—28no—
117#14556571—28no—
118#14556569—28no—
119#14556569—28no—
120#14556569—28no—
121#14556549—22no—
122#14556549C2314yes—
123#14556548D414yes—
124#14556548C2314yes—
125C2×C4⋊Dic73—21no—
126C2×C4⋊Dic73—21no—
127C2×C4⋊Dic73C2311yescharacteristic
128C2×C4⋊Dic73C2311yescharacteristic
129C2×#11924007—21no—
130C2×#11924007—21no—
131C2×#11924007—21no—
132C2×#11924007—21no—
133C2×#11924007—21no—
134C2×#11924007D411yescharacteristic
135C2×#11924007D411yescharacteristic
136C4⋊C4×D73—22no—
137C4⋊C4×D73C2314yes—
138C2×#11924005—21no—
139C2×#11924005—21no—
140C2×#11924005—21no—
141C2×#11924005—21no—
142C2×#11924005—21no—
143C2×#11924005D411yescharacteristic
144C2×#11924005D411yescharacteristic
145C2×C4×Dic73—21no—
146C2×C4×Dic73C2311yescharacteristic
147#14556516C2314yes—
148#14556516C2314yes—
149#14556515C2314yes—
150#14556515C2314yes—
151#14556515C2314yes—
152#14556515C2314yes—
153#14556514C2314yes—
154#14556514C2314yes—
155#14556513C2314yes—
156#14556513C2314yes—
157#14556511C2314yes—
158#14556511C2314yes—
159#14556501C2314yes—
160C4×#10596831C2314yes—
161C8×Dic73C2314yes—
162C22×Q8×C73C2311yescharacteristic
163C22×Q8×C73C2311yescharacteristic
164C22×C8×C73C2311yescharacteristic
165C22×C8×C73C2311yescharacteristic
166C4⋊Q8×C73—22no—
167C4⋊Q8×C73C2314yes—
168#125×C73—22no—
169#125×C73C2314yes—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73C2311yescharacteristic
175C2×C4⋊C4×C73C2311yescharacteristic
176C2×C42×C73C2311yescharacteristic
177#103×C73C2314yes—
178#103×C73C2314yes—
179#103×C73C2314yes—
180#103×C73C2314yes—
181#97×C73C2314yes—
182C23×D73—21no—
183C23×D73C2×D411yescharacteristic
184#11924029—28no—
185#11924029—28no—
186#11924029—48no—
187C2×Dic146—22no—
188C2×Dic146—22no—
189C2×Dic146—21no—
190C2×Dic146—24no—
191C2×Dic146—24no—
192C2×Dic146—24no—
193C2×Dic146—44no—
194C2×Dic146—82no—
195C2×Dic146—82no—
196C2×Dic146C2412yes—
197Q8×D73—28no—
198Q8×D73—28no—
199Q8×D73—48no—
200C2×D292—22no—
201C2×D292—22no—
202C2×D292—24no—
203C2×D292—21no—
204C2×D292—44no—
205C2×D292C2412yes—
206C22×Dic73—21no—
207C22×Dic73—21no—
208C22×Dic73—21no—
209C22×Dic73C2×D411yescharacteristic
210C22×Dic73C2×D411yescharacteristic
211C22×Dic73C2×D411yescharacteristic
212C2×C4×D73—24no—
213C2×C4×D73—24no—
214C2×C4×D73—24no—
215C2×C4×D73—44no—
216C2×C4×D73—44no—
217C2×C4×D73—82no—
218C2×C4×D73C2×D412yes—
219C2×C4×D73#4114yes—
220C2×C4×D73#4114yes—
221C2×C4×D73C2412yes—
222#11924011—28no—
223C2×#10596831—22no—
224C2×#10596831—22no—
225C2×#10596831C2412yes—
226C2×#10596831C2412yes—
227C8×D73—28no—
228C4⋊Dic73—21no—
229C4⋊Dic73—24no—
230C4⋊Dic73—21no—
231C4⋊Dic73—24no—
232C4⋊Dic73C2412yes—
233C4⋊Dic73C2412yes—
234#11924007—24no—
235#11924007—24no—
236#11924007—24no—
237#11924007—24no—
238#11924007—24no—
239#11924007C2×D414yes—
240#11924007C2×D414yes—
241#11924005—24no—
242#11924005—24no—
243#11924005—24no—
244#11924005—24no—
245#11924005—24no—
246#11924005C2×D414yes—
247#11924005C2×D414yes—
248C4×Dic73—24no—
249C4×Dic73C2×D412yes—
250C4×Dic73C2412yes—
251C2×Q8×C73—21no—
252C2×Q8×C73—21no—
253C2×Q8×C73—22no—
254C2×Q8×C73—22no—
255C2×Q8×C73—22no—
256C2×Q8×C73—22no—
257C2×Q8×C73C2412yes—
258C2×Q8×C73C2412yes—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73C2×D411yescharacteristic
264C22×C4×C73C2×D411yescharacteristic
265C22×C4×C73C2411yescharacteristic
266C2×C8×C73—22no—
267C2×C8×C73—22no—
268C2×C8×C73C2412yes—
269C2×C8×C73C2412yes—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—24no—
272C4⋊C4×C73—24no—
273C4⋊C4×C73—24no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73C2412yes—
277C4⋊C4×C73C2412yes—
278C42×C73C2×D412yes—
279C42×C73C2412yes—
280C23×C73C22×D411yescharacteristic
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—42no—
285C22×D73—42no—
286C22×D73—42no—
287C22×D73#12414yes—
288C22×D73C22×D412yes—
289Q8×C73—22no—
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—22no—
293Q8×C73—42no—
294Q8×C73—42no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—42no—
302C2×C4×C73—42no—
303C2×C4×C73—42no—
304C2×C4×C73—42no—
305C2×C4×C73C22×D412yes—
306C2×C4×C73C22×D412yes—
307C2×C4×C73C22×D411yescharacteristic
308C2×C4×C73C2×#4112yes—
309C2×C4×C73C2×#4112yes—
310C2×C4×C73C2511yescharacteristic
311C2×Dic73—22no—
312C2×Dic73—22no—
313C2×Dic73—22no—
314C2×Dic73—22no—
315C2×Dic73—22no—
316C2×Dic73—42no—
317C2×Dic73—42no—
318C2×Dic73—42no—
319C2×Dic73#12414yes—
320C2×Dic73C22×D412yes—
321C2×Dic73C22×D412yes—
322C2×Dic73C22×D412yes—
323D292—22no—
324D292—22no—
325D292—48no—
326D292—42no—
327C4×D73—48no—
328C4×D73—48no—
329C4×D73—84no—
330C4×D73#12418yes—
331C4×D73C2×#4114yes—
332C4×D73C2×#4114yes—
333Dic146—22no—
334Dic146—22no—
335Dic146—42no—
336Dic146—48no—
337Dic146—84no—
338Dic146—84no—
339C8×C73—22no—
340C8×C73—22no—
341#10596831—22no—
342#10596831—22no—
343C22×C73C2×#12412yes—
344C22×C73#57712yes—
345C22×C73#57812yes—
346C22×C73C23×D411yescharacteristic
347C2×D73—28no—
348C2×D73—22no—
349C2×D73—22no—
350C2×D73—42no—
351C2×D73—42no—
352C2×D73—42no—
353C2×D73—84no—
354C2×D73C2×#12414yes—
355C4×C73—22no—
356C4×C73—22no—
357C4×C73—42no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—42no—
361C4×C73C2×#12412yes—
362C4×C73C22×#4111yescharacteristic
363C4×C73C22×#4111yescharacteristic
364Dic73—22no—
365Dic73—22no—
366Dic73—42no—
367Dic73—42no—
368Dic73—42no—
369Dic73C2×#12414yes—
370C2×#3137—731nomaximal, Sylow
371C2×C73#313714yescomplemented
372C2×C73C22×#12411yescharacteristic
373C2×C73C2×#57711yescharacteristic
374C2×C73C2×#57811yescharacteristic
375D73—24no—
376D73—82no—
377C2×#544—731no—
378C2×#536—731no—
379#3137—7316no—
380C2×#491—731no—
381C2×#491D7311yescharacteristic, complemented
382C2×#489—731no—
383C2×#489—731no—
384C2×#488—731no—
385C2×#488—731no—
386C2×#487—731no—
387C2×#487—731no—
388C2×#417—731no—
389C2×#419—731no—
390C2×#416—731no—
391C22×#103—731no—
392C2×#405—731no—
393C73C2×#313711yescharacteristic, complemented, Sylow
394C22×#41—731no—
395C23×Q8—731no—
396C22×M16—731no—
397C23×C8—731no—
398#544—738no—
399#544—1464no—
400#536—738no—
401#536—1464no—
402C2×C4⋊Q8—731no—
403C2×C4⋊Q8—731no—
404C2×C4⋊Q8—731no—
405C2×C4⋊Q8—1461no—
406C2×C4⋊Q8C2×D7311yescharacteristic
407C2×#125—731no—
408C2×#125—1461no—
409C2×#125C2×D7311yescharacteristic
410C2×#124—731no—
411C2×#124—731no—
412C2×#123—1461no—
413C2×#123—1461no—
414C2×C22⋊Q8—1461no—
415C2×C22⋊Q8—1461no—
416C2×C22⋊Q8—1461no—
417C2×C22⋊Q8—1461no—
418C2×#117—731no—
419C2×#117—731no—
420C22×C4⋊C4—731no—
421#491—738no—
422#491C2×D7318yescomplemented
423#489—738no—
424#489—738no—
425#488—738no—
426#488—738no—
427#487—738no—
428#487—738no—
429#419—738no—
430#417—738no—
431#416—738no—
432C2×#103—731no—
433C2×#103—731no—
434C2×#103—731no—
435C2×#103—731no—
436C2×#103—731no—
437C2×#103—731no—
438C2×#103—731no—
439C2×#103—731no—
440C2×#103—738no—
441C2×#103C2×D7311yescharacteristic
442C2×#103C2×D7311yescharacteristic
443C2×#103C2×D7311yescharacteristic
444C2×#103C2×D7311yescharacteristic
445C2×#102—731no—
446C2×#102—731no—
447C2×#102—731no—
448C2×#102—731no—
449#405—738no—
450C2×#97—731no—
451C2×#97C2×D7311yescharacteristic
452C2×C4×C8—731no—
453C2×C4×C8—731no—
454C2×#41—734no—
455C2×#41—1464no—
456C2×#41—1464no—
457C2×#41—1462no—
458C22×Q8—734no—
459C22×Q8—731no—
460C22×Q8—1461no—
461C22×Q8—1461no—
462C22×Q8—1464no—
463C22×Q8—1464no—
464C22×Q8—1462no—
465C22×Q8—1461no—
466C22×Q8C22×D7311yescharacteristic
467C22×Q8C22×D7311yescharacteristic
468C22×D4—731no—
469C22×D4—1461no—
470C23×C4—731no—
471C23×C4—1461no—
472C23×C4—1461no—
473C23×C4—1461no—
474C2×M16—734no—
475C2×M16—1464no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—734no—
479C22×C8—1464no—
480C22×C8C22×D7311yescharacteristic
481C22×C8C22×D7311yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—734no—
484C4⋊Q8—734no—
485C4⋊Q8—734no—
486C4⋊Q8—1462no—
487C4⋊Q8—1462no—
488C4⋊Q8—1468no—
489C4⋊Q8—1462no—
490C4⋊Q8C22×D7314yes—
491#125—22no—
492#125—734no—
493#125—1462no—
494#125—1468no—
495#125C22×D7314yes—
496#124—734no—
497#124—734no—
498#124—1462no—
499#124—1462no—
500#123—1468no—
501#123—1468no—
502C22⋊Q8—1468no—
503C22⋊Q8—1468no—
504C22⋊Q8—1468no—
505C22⋊Q8—1468no—
506#117—734no—
507#117—734no—
508#117—734no—
509#117—1462no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—734no—
519C2×C4⋊C4—1462no—
520C2×C4⋊C4—1461no—
521C2×C4⋊C4—1461no—
522C2×C4⋊C4—1461no—
523C2×C4⋊C4—1461no—
524C2×C4⋊C4—1461no—
525C2×C4⋊C4—1461no—
526C2×C4⋊C4—1461no—
527C2×C4⋊C4C22×D7311yescharacteristic
528C2×C4⋊C4C22×D7311yescharacteristic
529C2×C22⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—1461no—
532C2×C22⋊C4—1461no—
533C2×C22⋊C4—1461no—
534C2×C22⋊C4—1461no—
535C2×C22⋊C4—1461no—
536C2×C42—731no—
537C2×C42—1461no—
538C2×C42C22×D7311yescharacteristic
539#103—734no—
540#103—734no—
541#103—734no—
542#103—734no—
543#103—734no—
544#103—734no—
545#103—734no—
546#103—734no—
547#103C22×D7314yes—
548#103C22×D7314yes—
549#103C22×D7314yes—
550#103C22×D7314yes—
551#102—734no—
552#102—734no—
553#102—734no—
554#102—734no—
555#97—734no—
556#97C22×D7314yes—
557C4×C8—734no—
558C4×C8—734no—
559C24—731no—
560C24—1461no—
561#41—2928no—
562#41—1468no—
563#41—1468no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—2924no—
571C2×Q8—2928no—
572C2×Q8—5842no—
573C2×Q8—5842no—
574C2×Q8—732no—
575C2×Q8—1464no—
576C2×Q8—1464no—
577C2×Q8—1468no—
578C2×Q8—1468no—
579C2×Q8—1462no—
580C2×Q8—1462no—
581C2×Q8—1461no—
582C2×Q8—1464no—
583C2×Q8C23×D7312yes—
584C2×Q8C23×D7312yes—
585C2×D4—2924no—
586C2×D4—732no—
587C2×D4—1464no—
588C2×D4—1461no—
589C2×D4—1462no—
590C2×D4—1462no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—2924no—
596C22×C4—2924no—
597C22×C4—5842no—
598C22×C4—731no—
599C22×C4—732no—
600C22×C4—734no—
601C22×C4—734no—
602C22×C4—732no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—1464no—
606C22×C4—1464no—
607C22×C4—1464no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4D4×D7311yescharacteristic
612C22×C4D4×D7311yescharacteristic
613C22×C4C23×D7311yescharacteristic
614M16—1468no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—732no—
618C2×C8—732no—
619C2×C8—1468no—
620C2×C8—1462no—
621C2×C8—1462no—
622C2×C8C23×D7312yes—
623C2×C8C23×D7312yes—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—734no—
631C4⋊C4—734no—
632C4⋊C4—732no—
633C4⋊C4—732no—
634C4⋊C4—1464no—
635C4⋊C4—1464no—
636C4⋊C4—1464no—
637C4⋊C4—1464no—
638C4⋊C4—1464no—
639C4⋊C4—1464no—
640C4⋊C4—1461no—
641C4⋊C4—1461no—
642C4⋊C4—1464no—
643C4⋊C4C23×D7312yes—
644C4⋊C4C23×D7312yes—
645C22⋊C4—734no—
646C22⋊C4—734no—
647C22⋊C4—1464no—
648C22⋊C4—1464no—
649C22⋊C4—1464no—
650C22⋊C4—1464no—
651C22⋊C4—1464no—
652C42—732no—
653C42—732no—
654C42—1464no—
655C42D4×D7312yes—
656C42C23×D7312yes—
657C23—2922no—
658C23—2922no—
659C23—2922no—
660C23—732no—
661C23—734no—
662C23—1462no—
663C23—1462no—
664C23—1462no—
665C23C2×D4×D7311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—42no—
672Q8—2928no—
673Q8—2922no—
674Q8—5844no—
675Q8—5844no—
676Q8—1462no—
677Q8—1462no—
678D4—2928no—
679D4—2922no—
680D4—1462no—
681D4—1462no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—2928no—
693C2×C4—2928no—
694C2×C4—2922no—
695C2×C4—2922no—
696C2×C4—2922no—
697C2×C4—5844no—
698C2×C4—732no—
699C2×C4—734no—
700C2×C4—734no—
701C2×C4—734no—
702C2×C4—738no—
703C2×C4—732no—
704C2×C4—732no—
705C2×C4—1462no—
706C2×C4—1462no—
707C2×C4—1462no—
708C2×C4—1462no—
709C2×C4—1462no—
710C2×C4C2×D4×D7312yes—
711C2×C4C2×D4×D7312yes—
712C2×C4C2×D4×D7311yescharacteristic
713C2×C4#41×D7312yes—
714C2×C4#41×D7312yes—
715C2×C4C24×D7311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1462no—
719C8—1462no—
720C22—2922no—
721C22—2922no—
722C22—2922no—
723C22—5844no—
724C22—734no—
725C22—1468no—
726C22—1462no—
727C22—1462no—
728C22#124×D7312yes—
729C22#1798939612yes—
730C22#1798940312yes—
731C22C22×D4×D7311yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—2922no—
739C4—2922no—
740C4—2922no—
741C4—734no—
742C4—1462no—
743C4—1462no—
744C4#124×D7312yes—
745C4C2×#41×D7311yescharacteristic
746C4C2×#41×D7311yescharacteristic
747C2—5842no—
748C2—1464no—
749C2#2262029714yesdirect product factor
750C2C2×#124×D7311yescharacteristic
751C2C2×#1798939611yescharacteristic
752C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#491×C73C2
socleC23×C73C22×D4
prime radicalC22×#11924029C22
hypercenterC2×#491D73
hypocenterC73C2×#3137
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989217C2semidirect
3. #22620297C2direct (N × H)
4. C2×#17988954C2semidirect
5. C2×#17988948C2semidirect
6. C2×#17988947C2semidirect
7. C2×#17988944C2semidirect
8. C2×#17988943C2semidirect
9. C2×#17988937C2semidirect
10. C2×#17988936C2semidirect
12. C2×#17988594C2semidirect
14. C2×#103×D73C2semidirect
15. C2×#17988544C2semidirect
16. C2×#491×C73C2semidirect
22. #17989217C22semidirect
42. #17988954C22semidirect
43. #17988948C22semidirect
44. #17988947C22semidirect
45. #17988944C22semidirect
46. #17988943C22semidirect
47. #17988937C22semidirect
48. #17988936C22semidirect
49. #17988594C22semidirect
60. #103×D73C22semidirect
65. #17988544C22semidirect
71. #491×C73C22semidirect
371. C2×C73#3137semidirect
381. C2×#491D73semidirect
393. C73C2×#3137semidirect
422. #491C2×D73semidirect
749. C2#22620297direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179892172
C2×#179891622
#226202972
C2×#179889542
C2×#179889482
C2×#179889472
C2×#179889442
C2×#179889432
C2×#179889372
C2×#179889362
C2×#179885872
C2×#179885942
C2×#179885822
C2×#103×D732
C2×#179885442
C2×#491×C732
C2×#313773